It's worth noting that you're applying an overly simplistic model of what noise cancellation (at the Bose/Sony level) actually entails. There's a lot of signal processing involved and it's exceedingly unlikely that the headphones are significantly increasing the amount of high frequency noise reaching your ears. (Some noise cancelling headphones even have a microphone on the inside, to measure what your ears hear.)
There are lots of other sources of pain, fatigue and discomfort, though. Essentially, since the noise cancellation isn't perfect, you can hear some subset of the sound, varying across the frequency spectrum. This can cause a feeling of being underwater, of having blocked ears or simply of having to listen more closely, all of which might cause ongoing muscle tension of different muscles.
On the good news side, a lot of people who find discomfort with one brand of noise-cancelling can find other brands fine, so it might be worth trying some other brands. (For Bose, the main similar-quality competitor is Sony.)
Finally, in the simplistic model, there does not have to be a delay. Sound only travels at 340 metres per second, so for every 10mm distance between the microphone and the emitter, one can have around 34 microseconds of processing time.
There are lots of other sources of pain, fatigue and discomfort, though. Essentially, since the noise cancellation isn't perfect, you can hear some subset of the sound, varying across the frequency spectrum. This can cause a feeling of being underwater, of having blocked ears or simply of having to listen more closely, all of which might cause ongoing muscle tension of different muscles.
On the good news side, a lot of people who find discomfort with one brand of noise-cancelling can find other brands fine, so it might be worth trying some other brands. (For Bose, the main similar-quality competitor is Sony.)
Finally, in the simplistic model, there does not have to be a delay. Sound only travels at 340 metres per second, so for every 10mm distance between the microphone and the emitter, one can have around 34 microseconds of processing time.